LMFDB - Embedded newform 1155.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.352076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 $ x^5 - x^4 - 8x^3 + 3x^2 + 8*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.567739$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52275 q^{2} +1.00000 q^{3} +4.36426 q^{4} -1.00000 q^{5} -2.52275 q^{6} +1.00000 q^{7} -5.96443 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.52275 q^{2} +1.00000 q^{3} +4.36426 q^{4} -1.00000 q^{5} -2.52275 q^{6} +1.00000 q^{7} -5.96443 q^{8} +1.00000 q^{9} +2.52275 q^{10} +1.00000 q^{11} +4.36426 q^{12} +5.44168 q^{13} -2.52275 q^{14} -1.00000 q^{15} +6.31823 q^{16} +1.41028 q^{17} -2.52275 q^{18} -1.36426 q^{19} -4.36426 q^{20} +1.00000 q^{21} -2.52275 q^{22} -8.40975 q^{23} -5.96443 q^{24} +1.00000 q^{25} -13.7280 q^{26} +1.00000 q^{27} +4.36426 q^{28} +8.75991 q^{29} +2.52275 q^{30} +3.60382 q^{31} -4.01045 q^{32} +1.00000 q^{33} -3.55779 q^{34} -1.00000 q^{35} +4.36426 q^{36} +3.48771 q^{37} +3.44168 q^{38} +5.44168 q^{39} +5.96443 q^{40} +10.4411 q^{41} -2.52275 q^{42} -11.5345 q^{43} +4.36426 q^{44} -1.00000 q^{45} +21.2157 q^{46} -8.21622 q^{47} +6.31823 q^{48} +1.00000 q^{49} -2.52275 q^{50} +1.41028 q^{51} +23.7489 q^{52} -5.31823 q^{53} -2.52275 q^{54} -1.00000 q^{55} -5.96443 q^{56} -1.36426 q^{57} -22.0991 q^{58} +7.07689 q^{59} -4.36426 q^{60} +3.52640 q^{61} -9.09152 q^{62} +1.00000 q^{63} -2.51910 q^{64} -5.44168 q^{65} -2.52275 q^{66} -1.09152 q^{67} +6.15484 q^{68} -8.40975 q^{69} +2.52275 q^{70} +4.69534 q^{71} -5.96443 q^{72} +7.31645 q^{73} -8.79860 q^{74} +1.00000 q^{75} -5.95397 q^{76} +1.00000 q^{77} -13.7280 q^{78} +4.55832 q^{79} -6.31823 q^{80} +1.00000 q^{81} -26.3404 q^{82} -9.51910 q^{83} +4.36426 q^{84} -1.41028 q^{85} +29.0985 q^{86} +8.75991 q^{87} -5.96443 q^{88} -16.7421 q^{89} +2.52275 q^{90} +5.44168 q^{91} -36.7023 q^{92} +3.60382 q^{93} +20.7275 q^{94} +1.36426 q^{95} -4.01045 q^{96} +16.2630 q^{97} -2.52275 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.52275	−1.78385	−0.891926	−	0.452181i	$-0.850646\pi$
$2$	−2.52275	−1.78385	−0.891926	+	0.452181i	$0.850646\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.36426	2.18213
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.52275	−1.02991
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.96443	−2.10874
$9$	1.00000	0.333333
$10$	2.52275	0.797763
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.36426	1.25985
$13$	5.44168	1.50925	0.754625	−	0.656156i	$-0.227819\pi$
$13$	5.44168	1.50925	0.754625	+	0.656156i	$0.227819\pi$
$14$	−2.52275	−0.674233
$15$	−1.00000	−0.258199
$16$	6.31823	1.57956
$17$	1.41028	0.342044	0.171022	−	0.985267i	$-0.445293\pi$
$17$	1.41028	0.342044	0.171022	+	0.985267i	$0.445293\pi$
$18$	−2.52275	−0.594617
$19$	−1.36426	−0.312982	−0.156491	−	0.987679i	$-0.550018\pi$
$19$	−1.36426	−0.312982	−0.156491	+	0.987679i	$0.550018\pi$
$20$	−4.36426	−0.975878
$21$	1.00000	0.218218
$22$	−2.52275	−0.537852
$23$	−8.40975	−1.75355	−0.876777	−	0.480896i	$-0.840311\pi$
$23$	−8.40975	−1.75355	−0.876777	+	0.480896i	$0.840311\pi$
$24$	−5.96443	−1.21748
$25$	1.00000	0.200000
$26$	−13.7280	−2.69228
$27$	1.00000	0.192450
$28$	4.36426	0.824767
$29$	8.75991	1.62667	0.813337	−	0.581792i	$-0.197648\pi$
$29$	8.75991	1.62667	0.813337	+	0.581792i	$0.197648\pi$
$30$	2.52275	0.460589
$31$	3.60382	0.647265	0.323632	−	0.946183i	$-0.395096\pi$
$31$	3.60382	0.647265	0.323632	+	0.946183i	$0.395096\pi$
$32$	−4.01045	−0.708955
$33$	1.00000	0.174078
$34$	−3.55779	−0.610156
$35$	−1.00000	−0.169031
$36$	4.36426	0.727376
$37$	3.48771	0.573375	0.286688	−	0.958024i	$-0.407446\pi$
$37$	3.48771	0.573375	0.286688	+	0.958024i	$0.407446\pi$
$38$	3.44168	0.558314
$39$	5.44168	0.871366
$40$	5.96443	0.943059
$41$	10.4411	1.63063	0.815317	−	0.579015i	$-0.196563\pi$
$41$	10.4411	1.63063	0.815317	+	0.579015i	$0.196563\pi$
$42$	−2.52275	−0.389268
$43$	−11.5345	−1.75899	−0.879494	−	0.475910i	$-0.842119\pi$
$43$	−11.5345	−1.75899	−0.879494	+	0.475910i	$0.842119\pi$
$44$	4.36426	0.657937
$45$	−1.00000	−0.149071
$46$	21.2157	3.12808
$47$	−8.21622	−1.19846	−0.599230	−	0.800577i	$-0.704526\pi$
$47$	−8.21622	−1.19846	−0.599230	+	0.800577i	$0.704526\pi$
$48$	6.31823	0.911958
$49$	1.00000	0.142857
$50$	−2.52275	−0.356770
$51$	1.41028	0.197479
$52$	23.7489	3.29338
$53$	−5.31823	−0.730515	−0.365258	−	0.930906i	$-0.619019\pi$
$53$	−5.31823	−0.730515	−0.365258	+	0.930906i	$0.619019\pi$
$54$	−2.52275	−0.343303
$55$	−1.00000	−0.134840
$56$	−5.96443	−0.797030
$57$	−1.36426	−0.180700
$58$	−22.0991	−2.90175
$59$	7.07689	0.921333	0.460666	−	0.887573i	$-0.347610\pi$
$59$	7.07689	0.921333	0.460666	+	0.887573i	$0.347610\pi$
$60$	−4.36426	−0.563423
$61$	3.52640	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$61$	3.52640	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$62$	−9.09152	−1.15462
$63$	1.00000	0.125988
$64$	−2.51910	−0.314888
$65$	−5.44168	−0.674957
$66$	−2.52275	−0.310529
$67$	−1.09152	−0.133351	−0.0666753	−	0.997775i	$-0.521239\pi$
$67$	−1.09152	−0.133351	−0.0666753	+	0.997775i	$0.521239\pi$
$68$	6.15484	0.746384
$69$	−8.40975	−1.01242
$70$	2.52275	0.301526
$71$	4.69534	0.557234	0.278617	−	0.960402i	$-0.410124\pi$
$71$	4.69534	0.557234	0.278617	+	0.960402i	$0.410124\pi$
$72$	−5.96443	−0.702915
$73$	7.31645	0.856326	0.428163	−	0.903702i	$-0.359161\pi$
$73$	7.31645	0.856326	0.428163	+	0.903702i	$0.359161\pi$
$74$	−8.79860	−1.02282
$75$	1.00000	0.115470
$76$	−5.95397	−0.682968
$77$	1.00000	0.113961
$78$	−13.7280	−1.55439
$79$	4.55832	0.512851	0.256426	−	0.966564i	$-0.417455\pi$
$79$	4.55832	0.512851	0.256426	+	0.966564i	$0.417455\pi$
$80$	−6.31823	−0.706400
$81$	1.00000	0.111111
$82$	−26.3404	−2.90881
$83$	−9.51910	−1.04486	−0.522429	−	0.852683i	$-0.674974\pi$
$83$	−9.51910	−1.04486	−0.522429	+	0.852683i	$0.674974\pi$
$84$	4.36426	0.476180
$85$	−1.41028	−0.152967
$86$	29.0985	3.13777
$87$	8.75991	0.939161
$88$	−5.96443	−0.635810
$89$	−16.7421	−1.77466	−0.887329	−	0.461137i	$-0.847442\pi$
$89$	−16.7421	−1.77466	−0.887329	+	0.461137i	$0.847442\pi$
$90$	2.52275	0.265921
$91$	5.44168	0.570443
$92$	−36.7023	−3.82648
$93$	3.60382	0.373698
$94$	20.7275	2.13787
$95$	1.36426	0.139970
$96$	−4.01045	−0.409315
$97$	16.2630	1.65125	0.825627	−	0.564216i	$-0.190821\pi$
$97$	16.2630	1.65125	0.825627	+	0.564216i	$0.190821\pi$
$98$	−2.52275	−0.254836
$99$	1.00000	0.100504
$100$	4.36426	0.436426
$101$	14.9816	1.49073	0.745365	−	0.666657i	$-0.232275\pi$
$101$	14.9816	1.49073	0.745365	+	0.666657i	$0.232275\pi$
$102$	−3.55779	−0.352274
$103$	2.07742	0.204694	0.102347	−	0.994749i	$-0.467365\pi$
$103$	2.07742	0.204694	0.102347	+	0.994749i	$0.467365\pi$
$104$	−32.4565	−3.18262
$105$	−1.00000	−0.0975900
$106$	13.4166	1.30313
$107$	13.3778	1.29328	0.646642	−	0.762794i	$-0.276173\pi$
$107$	13.3778	1.29328	0.646642	+	0.762794i	$0.276173\pi$
$108$	4.36426	0.419951
$109$	−10.2790	−0.984551	−0.492275	−	0.870439i	$-0.663835\pi$
$109$	−10.2790	−0.984551	−0.492275	+	0.870439i	$0.663835\pi$
$110$	2.52275	0.240535
$111$	3.48771	0.331038
$112$	6.31823	0.597017
$113$	8.29364	0.780200	0.390100	−	0.920772i	$-0.372440\pi$
$113$	8.29364	0.780200	0.390100	+	0.920772i	$0.372440\pi$
$114$	3.44168	0.322343
$115$	8.40975	0.784214
$116$	38.2305	3.54961
$117$	5.44168	0.503083
$118$	−17.8532	−1.64352
$119$	1.41028	0.129281
$120$	5.96443	0.544475
$121$	1.00000	0.0909091
$122$	−8.89621	−0.805425
$123$	10.4411	0.941447
$124$	15.7280	1.41241
$125$	−1.00000	−0.0894427
$126$	−2.52275	−0.224744
$127$	12.8687	1.14192	0.570958	−	0.820980i	$-0.306572\pi$
$127$	12.8687	1.14192	0.570958	+	0.820980i	$0.306572\pi$
$128$	14.3760	1.27067
$129$	−11.5345	−1.01555
$130$	13.7280	1.20402
$131$	11.4239	0.998107	0.499053	−	0.866571i	$-0.333681\pi$
$131$	11.4239	0.998107	0.499053	+	0.866571i	$0.333681\pi$
$132$	4.36426	0.379860
$133$	−1.36426	−0.118296
$134$	2.75364	0.237878
$135$	−1.00000	−0.0860663
$136$	−8.41154	−0.721283
$137$	7.61187	0.650326	0.325163	−	0.945658i	$-0.394581\pi$
$137$	7.61187	0.650326	0.325163	+	0.945658i	$0.394581\pi$
$138$	21.2157	1.80600
$139$	−9.31645	−0.790211	−0.395106	−	0.918636i	$-0.629292\pi$
$139$	−9.31645	−0.790211	−0.395106	+	0.918636i	$0.629292\pi$
$140$	−4.36426	−0.368847
$141$	−8.21622	−0.691931
$142$	−11.8452	−0.994024
$143$	5.44168	0.455056
$144$	6.31823	0.526519
$145$	−8.75991	−0.727471
$146$	−18.4576	−1.52756
$147$	1.00000	0.0824786
$148$	15.2212	1.25118
$149$	14.1370	1.15815	0.579075	−	0.815274i	$-0.303414\pi$
$149$	14.1370	1.15815	0.579075	+	0.815274i	$0.303414\pi$
$150$	−2.52275	−0.205982
$151$	−7.56585	−0.615700	−0.307850	−	0.951435i	$-0.599610\pi$
$151$	−7.56585	−0.615700	−0.307850	+	0.951435i	$0.599610\pi$
$152$	8.13702	0.659999
$153$	1.41028	0.114015
$154$	−2.52275	−0.203289
$155$	−3.60382	−0.289466
$156$	23.7489	1.90143
$157$	−21.5972	−1.72365	−0.861824	−	0.507208i	$-0.830678\pi$
$157$	−21.5972	−1.72365	−0.861824	+	0.507208i	$0.830678\pi$
$158$	−11.4995	−0.914851
$159$	−5.31823	−0.421763
$160$	4.01045	0.317054
$161$	−8.40975	−0.662781
$162$	−2.52275	−0.198206
$163$	17.0608	1.33631	0.668154	−	0.744023i	$-0.267085\pi$
$163$	17.0608	1.33631	0.668154	+	0.744023i	$0.267085\pi$
$164$	45.5679	3.55825
$165$	−1.00000	−0.0778499
$166$	24.0143	1.86387
$167$	0.866594	0.0670590	0.0335295	−	0.999438i	$-0.489325\pi$
$167$	0.866594	0.0670590	0.0335295	+	0.999438i	$0.489325\pi$
$168$	−5.96443	−0.460166
$169$	16.6119	1.27784
$170$	3.55779	0.272870
$171$	−1.36426	−0.104327
$172$	−50.3393	−3.83834
$173$	10.0628	0.765060	0.382530	−	0.923943i	$-0.375053\pi$
$173$	10.0628	0.765060	0.382530	+	0.923943i	$0.375053\pi$
$174$	−22.0991	−1.67532
$175$	1.00000	0.0755929
$176$	6.31823	0.476255
$177$	7.07689	0.531932
$178$	42.2361	3.16573
$179$	2.42024	0.180897	0.0904487	−	0.995901i	$-0.471170\pi$
$179$	2.42024	0.180897	0.0904487	+	0.995901i	$0.471170\pi$
$180$	−4.36426	−0.325293
$181$	2.54191	0.188939	0.0944693	−	0.995528i	$-0.469885\pi$
$181$	2.54191	0.188939	0.0944693	+	0.995528i	$0.469885\pi$
$182$	−13.7280	−1.01759
$183$	3.52640	0.260679
$184$	50.1594	3.69780
$185$	−3.48771	−0.256421
$186$	−9.09152	−0.666623
$187$	1.41028	0.103130
$188$	−35.8577	−2.61519
$189$	1.00000	0.0727393
$190$	−3.44168	−0.249686
$191$	24.0899	1.74309	0.871543	−	0.490319i	$-0.163120\pi$
$191$	24.0899	1.74309	0.871543	+	0.490319i	$0.163120\pi$
$192$	−2.51910	−0.181800
$193$	7.77401	0.559586	0.279793	−	0.960060i	$-0.409734\pi$
$193$	7.77401	0.559586	0.279793	+	0.960060i	$0.409734\pi$
$194$	−41.0274	−2.94559
$195$	−5.44168	−0.389687
$196$	4.36426	0.311733
$197$	−0.425797	−0.0303368	−0.0151684	−	0.999885i	$-0.504828\pi$
$197$	−0.425797	−0.0303368	−0.0151684	+	0.999885i	$0.504828\pi$
$198$	−2.52275	−0.179284
$199$	11.8200	0.837900	0.418950	−	0.908009i	$-0.362398\pi$
$199$	11.8200	0.837900	0.418950	+	0.908009i	$0.362398\pi$
$200$	−5.96443	−0.421749
$201$	−1.09152	−0.0769900
$202$	−37.7949	−2.65924
$203$	8.75991	0.614825
$204$	6.15484	0.430925
$205$	−10.4411	−0.729242
$206$	−5.24081	−0.365145
$207$	−8.40975	−0.584518
$208$	34.3818	2.38395
$209$	−1.36426	−0.0943677
$210$	2.52275	0.174086
$211$	−24.2305	−1.66810	−0.834049	−	0.551691i	$-0.813983\pi$
$211$	−24.2305	−1.66810	−0.834049	+	0.551691i	$0.813983\pi$
$212$	−23.2101	−1.59408
$213$	4.69534	0.321719
$214$	−33.7489	−2.30703
$215$	11.5345	0.786643
$216$	−5.96443	−0.405828
$217$	3.60382	0.244643
$218$	25.9314	1.75629
$219$	7.31645	0.494400
$220$	−4.36426	−0.294238
$221$	7.67431	0.516230
$222$	−8.79860	−0.590523
$223$	2.62289	0.175642	0.0878210	−	0.996136i	$-0.472010\pi$
$223$	2.62289	0.175642	0.0878210	+	0.996136i	$0.472010\pi$
$224$	−4.01045	−0.267960
$225$	1.00000	0.0666667
$226$	−20.9228	−1.39176
$227$	−3.02281	−0.200631	−0.100315	−	0.994956i	$-0.531985\pi$
$227$	−3.02281	−0.200631	−0.100315	+	0.994956i	$0.531985\pi$
$228$	−5.95397	−0.394312
$229$	−3.23725	−0.213923	−0.106962	−	0.994263i	$-0.534112\pi$
$229$	−3.23725	−0.213923	−0.106962	+	0.994263i	$0.534112\pi$
$230$	−21.2157	−1.39892
$231$	1.00000	0.0657952
$232$	−52.2479	−3.43024
$233$	−18.0363	−1.18159	−0.590797	−	0.806820i	$-0.701187\pi$
$233$	−18.0363	−1.18159	−0.590797	+	0.806820i	$0.701187\pi$
$234$	−13.7280	−0.897427
$235$	8.21622	0.535967
$236$	30.8854	2.01047
$237$	4.55832	0.296095
$238$	−3.55779	−0.230617
$239$	9.44346	0.610847	0.305423	−	0.952217i	$-0.401202\pi$
$239$	9.44346	0.610847	0.305423	+	0.952217i	$0.401202\pi$
$240$	−6.31823	−0.407840
$241$	16.7662	1.08001	0.540003	−	0.841663i	$-0.318423\pi$
$241$	16.7662	1.08001	0.540003	+	0.841663i	$0.318423\pi$
$242$	−2.52275	−0.162168
$243$	1.00000	0.0641500
$244$	15.3901	0.985250
$245$	−1.00000	−0.0638877
$246$	−26.3404	−1.67940
$247$	−7.42385	−0.472369
$248$	−21.4947	−1.36492
$249$	−9.51910	−0.603249
$250$	2.52275	0.159553
$251$	−27.8200	−1.75599	−0.877993	−	0.478674i	$-0.841118\pi$
$251$	−27.8200	−1.75599	−0.877993	+	0.478674i	$0.841118\pi$
$252$	4.36426	0.274922
$253$	−8.40975	−0.528717
$254$	−32.4646	−2.03701
$255$	−1.41028	−0.0883154
$256$	−31.2287	−1.95180
$257$	−13.5159	−0.843099	−0.421550	−	0.906805i	$-0.638514\pi$
$257$	−13.5159	−0.843099	−0.421550	+	0.906805i	$0.638514\pi$
$258$	29.0985	1.81159
$259$	3.48771	0.216715
$260$	−23.7489	−1.47284
$261$	8.75991	0.542225
$262$	−28.8195	−1.78048
$263$	−1.95397	−0.120487	−0.0602436	−	0.998184i	$-0.519188\pi$
$263$	−1.95397	−0.120487	−0.0602436	+	0.998184i	$0.519188\pi$
$264$	−5.96443	−0.367085
$265$	5.31823	0.326696
$266$	3.44168	0.211023
$267$	−16.7421	−1.02460
$268$	−4.76368	−0.290988
$269$	−12.2323	−0.745814	−0.372907	−	0.927869i	$-0.621639\pi$
$269$	−12.2323	−0.745814	−0.372907	+	0.927869i	$0.621639\pi$
$270$	2.52275	0.153530
$271$	−27.8877	−1.69406	−0.847028	−	0.531548i	$-0.821611\pi$
$271$	−27.8877	−1.69406	−0.847028	+	0.531548i	$0.821611\pi$
$272$	8.91050	0.540278
$273$	5.44168	0.329345
$274$	−19.2028	−1.16009
$275$	1.00000	0.0603023
$276$	−36.7023	−2.20922
$277$	−8.34518	−0.501413	−0.250707	−	0.968063i	$-0.580663\pi$
$277$	−8.34518	−0.501413	−0.250707	+	0.968063i	$0.580663\pi$
$278$	23.5031	1.40962
$279$	3.60382	0.215755
$280$	5.96443	0.356443
$281$	18.1998	1.08571	0.542855	−	0.839827i	$-0.317343\pi$
$281$	18.1998	1.08571	0.542855	+	0.839827i	$0.317343\pi$
$282$	20.7275	1.23430
$283$	−7.49021	−0.445247	−0.222623	−	0.974905i	$-0.571462\pi$
$283$	−7.49021	−0.445247	−0.222623	+	0.974905i	$0.571462\pi$
$284$	20.4917	1.21596
$285$	1.36426	0.0808117
$286$	−13.7280	−0.811753
$287$	10.4411	0.616322
$288$	−4.01045	−0.236318
$289$	−15.0111	−0.883006
$290$	22.0991	1.29770
$291$	16.2630	0.953352
$292$	31.9309	1.86861
$293$	−5.15983	−0.301440	−0.150720	−	0.988576i	$-0.548159\pi$
$293$	−5.15983	−0.301440	−0.150720	+	0.988576i	$0.548159\pi$
$294$	−2.52275	−0.147130
$295$	−7.07689	−0.412033
$296$	−20.8022	−1.20910
$297$	1.00000	0.0580259
$298$	−35.6641	−2.06597
$299$	−45.7632	−2.64655
$300$	4.36426	0.251971
$301$	−11.5345	−0.664835
$302$	19.0867	1.09832
$303$	14.9816	0.860673
$304$	−8.61970	−0.494374
$305$	−3.52640	−0.201921
$306$	−3.55779	−0.203385
$307$	16.8859	0.963727	0.481864	−	0.876246i	$-0.339960\pi$
$307$	16.8859	0.963727	0.481864	+	0.876246i	$0.339960\pi$
$308$	4.36426	0.248677
$309$	2.07742	0.118180
$310$	9.09152	0.516364
$311$	−15.0633	−0.854163	−0.427081	−	0.904213i	$-0.640458\pi$
$311$	−15.0633	−0.854163	−0.427081	+	0.904213i	$0.640458\pi$
$312$	−32.4565	−1.83749
$313$	−14.8687	−0.840430	−0.420215	−	0.907425i	$-0.638045\pi$
$313$	−14.8687	−0.840430	−0.420215	+	0.907425i	$0.638045\pi$
$314$	54.4844	3.07473
$315$	−1.00000	−0.0563436
$316$	19.8937	1.11911
$317$	31.0015	1.74122	0.870609	−	0.491976i	$-0.163725\pi$
$317$	31.0015	1.74122	0.870609	+	0.491976i	$0.163725\pi$
$318$	13.4166	0.752363
$319$	8.75991	0.490461
$320$	2.51910	0.140822
$321$	13.3778	0.746678
$322$	21.2157	1.18230
$323$	−1.92399	−0.107054
$324$	4.36426	0.242459
$325$	5.44168	0.301850
$326$	−43.0402	−2.38378
$327$	−10.2790	−0.568431
$328$	−62.2755	−3.43859
$329$	−8.21622	−0.452975
$330$	2.52275	0.138873
$331$	13.6597	0.750804	0.375402	−	0.926862i	$-0.377505\pi$
$331$	13.6597	0.750804	0.375402	+	0.926862i	$0.377505\pi$
$332$	−41.5438	−2.28001
$333$	3.48771	0.191125
$334$	−2.18620	−0.119623
$335$	1.09152	0.0596362
$336$	6.31823	0.344688
$337$	−21.3060	−1.16061	−0.580305	−	0.814399i	$-0.697067\pi$
$337$	−21.3060	−1.16061	−0.580305	+	0.814399i	$0.697067\pi$
$338$	−41.9076	−2.27947
$339$	8.29364	0.450449
$340$	−6.15484	−0.333793
$341$	3.60382	0.195158
$342$	3.44168	0.186105
$343$	1.00000	0.0539949
$344$	68.7964	3.70925
$345$	8.40975	0.452766
$346$	−25.3859	−1.36475
$347$	−28.6358	−1.53725	−0.768626	−	0.639699i	$-0.779059\pi$
$347$	−28.6358	−1.53725	−0.768626	+	0.639699i	$0.779059\pi$
$348$	38.2305	2.04937
$349$	−4.50075	−0.240919	−0.120460	−	0.992718i	$-0.538437\pi$
$349$	−4.50075	−0.240919	−0.120460	+	0.992718i	$0.538437\pi$
$350$	−2.52275	−0.134847
$351$	5.44168	0.290455
$352$	−4.01045	−0.213758
$353$	−7.51838	−0.400163	−0.200081	−	0.979779i	$-0.564121\pi$
$353$	−7.51838	−0.400163	−0.200081	+	0.979779i	$0.564121\pi$
$354$	−17.8532	−0.948888
$355$	−4.69534	−0.249203
$356$	−73.0668	−3.87253
$357$	1.41028	0.0746401
$358$	−6.10566	−0.322694
$359$	−24.7410	−1.30578	−0.652891	−	0.757452i	$-0.726444\pi$
$359$	−24.7410	−1.30578	−0.652891	+	0.757452i	$0.726444\pi$
$360$	5.96443	0.314353
$361$	−17.1388	−0.902042
$362$	−6.41260	−0.337039
$363$	1.00000	0.0524864
$364$	23.7489	1.24478
$365$	−7.31645	−0.382961
$366$	−8.89621	−0.465012
$367$	16.6782	0.870597	0.435298	−	0.900286i	$-0.356643\pi$
$367$	16.6782	0.870597	0.435298	+	0.900286i	$0.356643\pi$
$368$	−53.1348	−2.76984
$369$	10.4411	0.543545
$370$	8.79860	0.457418
$371$	−5.31823	−0.276109
$372$	15.7280	0.815458
$373$	−18.1757	−0.941103	−0.470551	−	0.882373i	$-0.655945\pi$
$373$	−18.1757	−0.941103	−0.470551	+	0.882373i	$0.655945\pi$
$374$	−3.55779	−0.183969
$375$	−1.00000	−0.0516398
$376$	49.0051	2.52724
$377$	47.6686	2.45506
$378$	−2.52275	−0.129756
$379$	−3.31823	−0.170446	−0.0852231	−	0.996362i	$-0.527160\pi$
$379$	−3.31823	−0.170446	−0.0852231	+	0.996362i	$0.527160\pi$
$380$	5.95397	0.305432
$381$	12.8687	0.659285
$382$	−60.7728	−3.10941
$383$	18.6205	0.951461	0.475731	−	0.879591i	$-0.342184\pi$
$383$	18.6205	0.951461	0.475731	+	0.879591i	$0.342184\pi$
$384$	14.3760	0.733620
$385$	−1.00000	−0.0509647
$386$	−19.6119	−0.998218
$387$	−11.5345	−0.586329
$388$	70.9758	3.60325
$389$	−9.64505	−0.489024	−0.244512	−	0.969646i	$-0.578628\pi$
$389$	−9.64505	−0.489024	−0.244512	+	0.969646i	$0.578628\pi$
$390$	13.7280	0.695144
$391$	−11.8601	−0.599793
$392$	−5.96443	−0.301249
$393$	11.4239	0.576257
$394$	1.07418	0.0541163
$395$	−4.55832	−0.229354
$396$	4.36426	0.219312
$397$	−22.9451	−1.15158	−0.575791	−	0.817597i	$-0.695306\pi$
$397$	−22.9451	−1.15158	−0.575791	+	0.817597i	$0.695306\pi$
$398$	−29.8190	−1.49469
$399$	−1.36426	−0.0682983
$400$	6.31823	0.315912
$401$	17.4239	0.870106	0.435053	−	0.900405i	$-0.356730\pi$
$401$	17.4239	0.870106	0.435053	+	0.900405i	$0.356730\pi$
$402$	2.75364	0.137339
$403$	19.6108	0.976884
$404$	65.3838	3.25296
$405$	−1.00000	−0.0496904
$406$	−22.0991	−1.09676
$407$	3.48771	0.172879
$408$	−8.41154	−0.416433
$409$	−1.21816	−0.0602343	−0.0301172	−	0.999546i	$-0.509588\pi$
$409$	−1.21816	−0.0602343	−0.0301172	+	0.999546i	$0.509588\pi$
$410$	26.3404	1.30086
$411$	7.61187	0.375466
$412$	9.06640	0.446670
$413$	7.07689	0.348231
$414$	21.2157	1.04269
$415$	9.51910	0.467274
$416$	−21.8236	−1.06999
$417$	−9.31645	−0.456229
$418$	3.44168	0.168338
$419$	2.35088	0.114848	0.0574240	−	0.998350i	$-0.481711\pi$
$419$	2.35088	0.114848	0.0574240	+	0.998350i	$0.481711\pi$
$420$	−4.36426	−0.212954
$421$	−18.9572	−0.923920	−0.461960	−	0.886901i	$-0.652854\pi$
$421$	−18.9572	−0.923920	−0.461960	+	0.886901i	$0.652854\pi$
$422$	61.1275	2.97564
$423$	−8.21622	−0.399486
$424$	31.7202	1.54047
$425$	1.41028	0.0684088
$426$	−11.8452	−0.573900
$427$	3.52640	0.170654
$428$	58.3843	2.82211
$429$	5.44168	0.262727
$430$	−29.0985	−1.40326
$431$	32.8823	1.58388	0.791942	−	0.610596i	$-0.209070\pi$
$431$	32.8823	1.58388	0.791942	+	0.610596i	$0.209070\pi$
$432$	6.31823	0.303986
$433$	−9.33322	−0.448526	−0.224263	−	0.974529i	$-0.571997\pi$
$433$	−9.33322	−0.448526	−0.224263	+	0.974529i	$0.571997\pi$
$434$	−9.09152	−0.436407
$435$	−8.75991	−0.420006
$436$	−44.8603	−2.14842
$437$	11.4731	0.548832
$438$	−18.4576	−0.881936
$439$	16.7010	0.797097	0.398549	−	0.917147i	$-0.369514\pi$
$439$	16.7010	0.797097	0.398549	+	0.917147i	$0.369514\pi$
$440$	5.96443	0.284343
$441$	1.00000	0.0476190
$442$	−19.3604	−0.920878
$443$	−9.79184	−0.465224	−0.232612	−	0.972570i	$-0.574727\pi$
$443$	−9.79184	−0.465224	−0.232612	+	0.972570i	$0.574727\pi$
$444$	15.2212	0.722368
$445$	16.7421	0.793651
$446$	−6.61690	−0.313319
$447$	14.1370	0.668658
$448$	−2.51910	−0.119016
$449$	−36.5556	−1.72516	−0.862582	−	0.505918i	$-0.831154\pi$
$449$	−36.5556	−1.72516	−0.862582	+	0.505918i	$0.831154\pi$
$450$	−2.52275	−0.118923
$451$	10.4411	0.491655
$452$	36.1956	1.70250
$453$	−7.56585	−0.355475
$454$	7.62578	0.357896
$455$	−5.44168	−0.255110
$456$	8.13702	0.381051
$457$	−18.7986	−0.879363	−0.439682	−	0.898154i	$-0.644909\pi$
$457$	−18.7986	−0.879363	−0.439682	+	0.898154i	$0.644909\pi$
$458$	8.16676	0.381608
$459$	1.41028	0.0658264
$460$	36.7023	1.71126
$461$	34.0972	1.58807	0.794033	−	0.607875i	$-0.207978\pi$
$461$	34.0972	1.58807	0.794033	+	0.607875i	$0.207978\pi$
$462$	−2.52275	−0.117369
$463$	−6.20816	−0.288518	−0.144259	−	0.989540i	$-0.546080\pi$
$463$	−6.20816	−0.288518	−0.144259	+	0.989540i	$0.546080\pi$
$464$	55.3472	2.56943
$465$	−3.60382	−0.167123
$466$	45.5009	2.10779
$467$	3.20763	0.148432	0.0742158	−	0.997242i	$-0.476355\pi$
$467$	3.20763	0.148432	0.0742158	+	0.997242i	$0.476355\pi$
$468$	23.7489	1.09779
$469$	−1.09152	−0.0504018
$470$	−20.7275	−0.956086
$471$	−21.5972	−0.995149
$472$	−42.2096	−1.94285
$473$	−11.5345	−0.530355
$474$	−11.4995	−0.528189
$475$	−1.36426	−0.0625965
$476$	6.15484	0.282107
$477$	−5.31823	−0.243505
$478$	−23.8235	−1.08966
$479$	−10.1252	−0.462634	−0.231317	−	0.972878i	$-0.574303\pi$
$479$	−10.1252	−0.462634	−0.231317	+	0.972878i	$0.574303\pi$
$480$	4.01045	0.183051
$481$	18.9790	0.865367
$482$	−42.2969	−1.92657
$483$	−8.40975	−0.382657
$484$	4.36426	0.198375
$485$	−16.2630	−0.738463
$486$	−2.52275	−0.114434
$487$	−25.5721	−1.15878	−0.579391	−	0.815050i	$-0.696710\pi$
$487$	−25.5721	−1.15878	−0.579391	+	0.815050i	$0.696710\pi$
$488$	−21.0329	−0.952116
$489$	17.0608	0.771518
$490$	2.52275	0.113966
$491$	−15.4681	−0.698066	−0.349033	−	0.937111i	$-0.613490\pi$
$491$	−15.4681	−0.698066	−0.349033	+	0.937111i	$0.613490\pi$
$492$	45.5679	2.05436
$493$	12.3540	0.556394
$494$	18.7285	0.842636
$495$	−1.00000	−0.0449467
$496$	22.7698	1.02239
$497$	4.69534	0.210615
$498$	24.0143	1.07611
$499$	−0.712473	−0.0318947	−0.0159473	−	0.999873i	$-0.505076\pi$
$499$	−0.712473	−0.0318947	−0.0159473	+	0.999873i	$0.505076\pi$
$500$	−4.36426	−0.195176
$501$	0.866594	0.0387165
$502$	70.1829	3.13242
$503$	−41.8595	−1.86642	−0.933211	−	0.359328i	$-0.883006\pi$
$503$	−41.8595	−1.86642	−0.933211	+	0.359328i	$0.883006\pi$
$504$	−5.96443	−0.265677
$505$	−14.9816	−0.666674
$506$	21.2157	0.943153
$507$	16.6119	0.737759
$508$	56.1625	2.49181
$509$	5.35247	0.237244	0.118622	−	0.992939i	$-0.462152\pi$
$509$	5.35247	0.237244	0.118622	+	0.992939i	$0.462152\pi$
$510$	3.55779	0.157542
$511$	7.31645	0.323661
$512$	50.0303	2.21105
$513$	−1.36426	−0.0602335
$514$	34.0972	1.50396
$515$	−2.07742	−0.0915421
$516$	−50.3393	−2.21607
$517$	−8.21622	−0.361349
$518$	−8.79860	−0.386588
$519$	10.0628	0.441708
$520$	32.4565	1.42331
$521$	−18.6511	−0.817119	−0.408560	−	0.912732i	$-0.633969\pi$
$521$	−18.6511	−0.817119	−0.408560	+	0.912732i	$0.633969\pi$
$522$	−22.0991	−0.967249
$523$	−26.2494	−1.14781	−0.573903	−	0.818923i	$-0.694571\pi$
$523$	−26.2494	−1.14781	−0.573903	+	0.818923i	$0.694571\pi$
$524$	49.8567	2.17800
$525$	1.00000	0.0436436
$526$	4.92938	0.214931
$527$	5.08240	0.221393
$528$	6.31823	0.274966
$529$	47.7240	2.07496
$530$	−13.4166	−0.582778
$531$	7.07689	0.307111
$532$	−5.95397	−0.258138
$533$	56.8174	2.46103
$534$	42.2361	1.82773
$535$	−13.3778	−0.578374
$536$	6.51030	0.281202
$537$	2.42024	0.104441
$538$	30.8589	1.33042
$539$	1.00000	0.0430730
$540$	−4.36426	−0.187808
$541$	23.0714	0.991916	0.495958	−	0.868346i	$-0.334817\pi$
$541$	23.0714	0.991916	0.495958	+	0.868346i	$0.334817\pi$
$542$	70.3536	3.02195
$543$	2.54191	0.109084
$544$	−5.65588	−0.242494
$545$	10.2790	0.440305
$546$	−13.7280	−0.587504
$547$	43.1117	1.84332	0.921662	−	0.387993i	$-0.126831\pi$
$547$	43.1117	1.84332	0.921662	+	0.387993i	$0.126831\pi$
$548$	33.2202	1.41910
$549$	3.52640	0.150503
$550$	−2.52275	−0.107570
$551$	−11.9508	−0.509120
$552$	50.1594	2.13492
$553$	4.55832	0.193840
$554$	21.0528	0.894447
$555$	−3.48771	−0.148045
$556$	−40.6594	−1.72434
$557$	5.15537	0.218440	0.109220	−	0.994018i	$-0.465165\pi$
$557$	5.15537	0.218440	0.109220	+	0.994018i	$0.465165\pi$
$558$	−9.09152	−0.384875
$559$	−62.7668	−2.65475
$560$	−6.31823	−0.266994
$561$	1.41028	0.0595422
$562$	−45.9135	−1.93675
$563$	−31.7624	−1.33863	−0.669313	−	0.742980i	$-0.733412\pi$
$563$	−31.7624	−1.33863	−0.669313	+	0.742980i	$0.733412\pi$
$564$	−35.8577	−1.50988
$565$	−8.29364	−0.348916
$566$	18.8959	0.794254
$567$	1.00000	0.0419961
$568$	−28.0050	−1.17506
$569$	−24.5256	−1.02817	−0.514083	−	0.857741i	$-0.671868\pi$
$569$	−24.5256	−1.02817	−0.514083	+	0.857741i	$0.671868\pi$
$570$	−3.44168	−0.144156
$571$	14.8077	0.619684	0.309842	−	0.950788i	$-0.399724\pi$
$571$	14.8077	0.619684	0.309842	+	0.950788i	$0.399724\pi$
$572$	23.7489	0.992991
$573$	24.0899	1.00637
$574$	−26.3404	−1.09943
$575$	−8.40975	−0.350711
$576$	−2.51910	−0.104963
$577$	−17.3304	−0.721474	−0.360737	−	0.932668i	$-0.617475\pi$
$577$	−17.3304	−0.721474	−0.360737	+	0.932668i	$0.617475\pi$
$578$	37.8692	1.57515
$579$	7.77401	0.323077
$580$	−38.2305	−1.58744
$581$	−9.51910	−0.394919
$582$	−41.0274	−1.70064
$583$	−5.31823	−0.220259
$584$	−43.6384	−1.80577
$585$	−5.44168	−0.224986
$586$	13.0169	0.537725
$587$	45.9180	1.89524	0.947620	−	0.319400i	$-0.103481\pi$
$587$	45.9180	1.89524	0.947620	+	0.319400i	$0.103481\pi$
$588$	4.36426	0.179979
$589$	−4.91654	−0.202582
$590$	17.8532	0.735005
$591$	−0.425797	−0.0175150
$592$	22.0361	0.905679
$593$	1.54658	0.0635104	0.0317552	−	0.999496i	$-0.489890\pi$
$593$	1.54658	0.0635104	0.0317552	+	0.999496i	$0.489890\pi$
$594$	−2.52275	−0.103510
$595$	−1.41028	−0.0578160
$596$	61.6976	2.52723
$597$	11.8200	0.483762
$598$	115.449	4.72106
$599$	−18.2604	−0.746101	−0.373050	−	0.927811i	$-0.621688\pi$
$599$	−18.2604	−0.746101	−0.373050	+	0.927811i	$0.621688\pi$
$600$	−5.96443	−0.243497
$601$	−20.0990	−0.819856	−0.409928	−	0.912118i	$-0.634446\pi$
$601$	−20.0990	−0.819856	−0.409928	+	0.912118i	$0.634446\pi$
$602$	29.0985	1.18597
$603$	−1.09152	−0.0444502
$604$	−33.0193	−1.34354
$605$	−1.00000	−0.0406558
$606$	−37.7949	−1.53531
$607$	19.3368	0.784856	0.392428	−	0.919783i	$-0.371635\pi$
$607$	19.3368	0.784856	0.392428	+	0.919783i	$0.371635\pi$
$608$	5.47129	0.221890
$609$	8.75991	0.354970
$610$	8.89621	0.360197
$611$	−44.7100	−1.80877
$612$	6.15484	0.248795
$613$	41.1982	1.66398	0.831990	−	0.554790i	$-0.187202\pi$
$613$	41.1982	1.66398	0.831990	+	0.554790i	$0.187202\pi$
$614$	−42.5988	−1.71915
$615$	−10.4411	−0.421028
$616$	−5.96443	−0.240314
$617$	−3.17943	−0.127999	−0.0639996	−	0.997950i	$-0.520386\pi$
$617$	−3.17943	−0.127999	−0.0639996	+	0.997950i	$0.520386\pi$
$618$	−5.24081	−0.210816
$619$	−36.5831	−1.47040	−0.735200	−	0.677850i	$-0.762912\pi$
$619$	−36.5831	−1.47040	−0.735200	+	0.677850i	$0.762912\pi$
$620$	−15.7280	−0.631651
$621$	−8.40975	−0.337472
$622$	38.0010	1.52370
$623$	−16.7421	−0.670758
$624$	34.3818	1.37637
$625$	1.00000	0.0400000
$626$	37.5101	1.49920
$627$	−1.36426	−0.0544832
$628$	−94.2559	−3.76122
$629$	4.91865	0.196120
$630$	2.52275	0.100509
$631$	26.8209	1.06772	0.533861	−	0.845572i	$-0.320740\pi$
$631$	26.8209	1.06772	0.533861	+	0.845572i	$0.320740\pi$
$632$	−27.1878	−1.08147
$633$	−24.2305	−0.963077
$634$	−78.2090	−3.10607
$635$	−12.8687	−0.510680
$636$	−23.2101	−0.920342
$637$	5.44168	0.215607
$638$	−22.0991	−0.874910
$639$	4.69534	0.185745
$640$	−14.3760	−0.568260
$641$	10.1841	0.402248	0.201124	−	0.979566i	$-0.435541\pi$
$641$	10.1841	0.402248	0.201124	+	0.979566i	$0.435541\pi$
$642$	−33.7489	−1.33196
$643$	−15.3525	−0.605442	−0.302721	−	0.953079i	$-0.597895\pi$
$643$	−15.3525	−0.605442	−0.302721	+	0.953079i	$0.597895\pi$
$644$	−36.7023	−1.44627
$645$	11.5345	0.454169
$646$	4.85374	0.190968
$647$	−38.5234	−1.51451	−0.757256	−	0.653118i	$-0.773461\pi$
$647$	−38.5234	−1.51451	−0.757256	+	0.653118i	$0.773461\pi$
$648$	−5.96443	−0.234305
$649$	7.07689	0.277792
$650$	−13.7280	−0.538456
$651$	3.60382	0.141245
$652$	74.4579	2.91600
$653$	4.17089	0.163219	0.0816097	−	0.996664i	$-0.473994\pi$
$653$	4.17089	0.163219	0.0816097	+	0.996664i	$0.473994\pi$
$654$	25.9314	1.01400
$655$	−11.4239	−0.446367
$656$	65.9696	2.57568
$657$	7.31645	0.285442
$658$	20.7275	0.808040
$659$	−38.1242	−1.48511	−0.742555	−	0.669785i	$-0.766386\pi$
$659$	−38.1242	−1.48511	−0.742555	+	0.669785i	$0.766386\pi$
$660$	−4.36426	−0.169879
$661$	−28.4621	−1.10705	−0.553523	−	0.832834i	$-0.686717\pi$
$661$	−28.4621	−1.10705	−0.553523	+	0.832834i	$0.686717\pi$
$662$	−34.4599	−1.33932
$663$	7.67431	0.298046
$664$	56.7760	2.20334
$665$	1.36426	0.0529037
$666$	−8.79860	−0.340939
$667$	−73.6687	−2.85246
$668$	3.78204	0.146331
$669$	2.62289	0.101407
$670$	−2.75364	−0.106382
$671$	3.52640	0.136135
$672$	−4.01045	−0.154707
$673$	−18.4890	−0.712697	−0.356348	−	0.934353i	$-0.615978\pi$
$673$	−18.4890	−0.712697	−0.356348	+	0.934353i	$0.615978\pi$
$674$	53.7496	2.07036
$675$	1.00000	0.0384900
$676$	72.4985	2.78840
$677$	8.58721	0.330033	0.165017	−	0.986291i	$-0.447232\pi$
$677$	8.58721	0.330033	0.165017	+	0.986291i	$0.447232\pi$
$678$	−20.9228	−0.803534
$679$	16.2630	0.624115
$680$	8.41154	0.322568
$681$	−3.02281	−0.115834
$682$	−9.09152	−0.348132
$683$	4.05226	0.155055	0.0775277	−	0.996990i	$-0.475297\pi$
$683$	4.05226	0.155055	0.0775277	+	0.996990i	$0.475297\pi$
$684$	−5.95397	−0.227656
$685$	−7.61187	−0.290835
$686$	−2.52275	−0.0963190
$687$	−3.23725	−0.123509
$688$	−72.8774	−2.77842
$689$	−28.9401	−1.10253
$690$	−21.2157	−0.807668
$691$	−0.408622	−0.0155447	−0.00777235	−	0.999970i	$-0.502474\pi$
$691$	−0.408622	−0.0155447	−0.00777235	+	0.999970i	$0.502474\pi$
$692$	43.9166	1.66946
$693$	1.00000	0.0379869
$694$	72.2409	2.74223
$695$	9.31645	0.353393
$696$	−52.2479	−1.98045
$697$	14.7250	0.557749
$698$	11.3543	0.429765
$699$	−18.0363	−0.682194
$700$	4.36426	0.164953
$701$	−37.1239	−1.40215	−0.701075	−	0.713088i	$-0.747296\pi$
$701$	−37.1239	−1.40215	−0.701075	+	0.713088i	$0.747296\pi$
$702$	−13.7280	−0.518129
$703$	−4.75813	−0.179456
$704$	−2.51910	−0.0949422
$705$	8.21622	0.309441
$706$	18.9670	0.713832
$707$	14.9816	0.563443
$708$	30.8854	1.16074
$709$	−3.88834	−0.146030	−0.0730149	−	0.997331i	$-0.523262\pi$
$709$	−3.88834	−0.146030	−0.0730149	+	0.997331i	$0.523262\pi$
$710$	11.8452	0.444541
$711$	4.55832	0.170950
$712$	99.8570	3.74230
$713$	−30.3072	−1.13501
$714$	−3.55779	−0.133147
$715$	−5.44168	−0.203507
$716$	10.5626	0.394742
$717$	9.44346	0.352673
$718$	62.4154	2.32932
$719$	−25.8792	−0.965132	−0.482566	−	0.875860i	$-0.660295\pi$
$719$	−25.8792	−0.965132	−0.482566	+	0.875860i	$0.660295\pi$
$720$	−6.31823	−0.235467
$721$	2.07742	0.0773672
$722$	43.2369	1.60911
$723$	16.7662	0.623541
$724$	11.0935	0.412288
$725$	8.75991	0.325335
$726$	−2.52275	−0.0936280
$727$	−12.9315	−0.479604	−0.239802	−	0.970822i	$-0.577082\pi$
$727$	−12.9315	−0.479604	−0.239802	+	0.970822i	$0.577082\pi$
$728$	−32.4565	−1.20292
$729$	1.00000	0.0370370
$730$	18.4576	0.683145
$731$	−16.2669	−0.601651
$732$	15.3901	0.568834
$733$	34.2270	1.26420	0.632101	−	0.774886i	$-0.282193\pi$
$733$	34.2270	1.26420	0.632101	+	0.774886i	$0.282193\pi$
$734$	−42.0750	−1.55302
$735$	−1.00000	−0.0368856
$736$	33.7269	1.24319
$737$	−1.09152	−0.0402067
$738$	−26.3404	−0.969603
$739$	−12.1741	−0.447832	−0.223916	−	0.974608i	$-0.571884\pi$
$739$	−12.1741	−0.447832	−0.223916	+	0.974608i	$0.571884\pi$
$740$	−15.2212	−0.559544
$741$	−7.42385	−0.272722
$742$	13.4166	0.492537
$743$	−14.2672	−0.523414	−0.261707	−	0.965147i	$-0.584285\pi$
$743$	−14.2672	−0.523414	−0.261707	+	0.965147i	$0.584285\pi$
$744$	−21.4947	−0.788034
$745$	−14.1370	−0.517940
$746$	45.8527	1.67879
$747$	−9.51910	−0.348286
$748$	6.15484	0.225043
$749$	13.3778	0.488815
$750$	2.52275	0.0921177
$751$	−31.9793	−1.16694	−0.583471	−	0.812134i	$-0.698306\pi$
$751$	−31.9793	−1.16694	−0.583471	+	0.812134i	$0.698306\pi$
$752$	−51.9120	−1.89304
$753$	−27.8200	−1.01382
$754$	−120.256	−4.37946
$755$	7.56585	0.275349
$756$	4.36426	0.158727
$757$	14.4681	0.525852	0.262926	−	0.964816i	$-0.415313\pi$
$757$	14.4681	0.525852	0.262926	+	0.964816i	$0.415313\pi$
$758$	8.37106	0.304051
$759$	−8.40975	−0.305255
$760$	−8.13702	−0.295161
$761$	−26.5297	−0.961700	−0.480850	−	0.876803i	$-0.659672\pi$
$761$	−26.5297	−0.961700	−0.480850	+	0.876803i	$0.659672\pi$
$762$	−32.4646	−1.17607
$763$	−10.2790	−0.372125
$764$	105.135	3.80364
$765$	−1.41028	−0.0509889
$766$	−46.9747	−1.69727
$767$	38.5102	1.39052
$768$	−31.2287	−1.12687
$769$	−36.1744	−1.30448	−0.652240	−	0.758012i	$-0.726171\pi$
$769$	−36.1744	−1.30448	−0.652240	+	0.758012i	$0.726171\pi$
$770$	2.52275	0.0909135
$771$	−13.5159	−0.486763
$772$	33.9278	1.22109
$773$	4.48162	0.161193	0.0805964	−	0.996747i	$-0.474318\pi$
$773$	4.48162	0.161193	0.0805964	+	0.996747i	$0.474318\pi$
$774$	29.0985	1.04592
$775$	3.60382	0.129453
$776$	−96.9993	−3.48207
$777$	3.48771	0.125121
$778$	24.3320	0.872346
$779$	−14.2444	−0.510359
$780$	−23.7489	−0.850347
$781$	4.69534	0.168012
$782$	29.9201	1.06994
$783$	8.75991	0.313054
$784$	6.31823	0.225651
$785$	21.5972	0.770839
$786$	−28.8195	−1.02796
$787$	32.7728	1.16823	0.584113	−	0.811673i	$-0.301443\pi$
$787$	32.7728	1.16823	0.584113	+	0.811673i	$0.301443\pi$
$788$	−1.85829	−0.0661988
$789$	−1.95397	−0.0695633
$790$	11.4995	0.409134
$791$	8.29364	0.294888
$792$	−5.96443	−0.211937
$793$	19.1895	0.681440
$794$	57.8847	2.05425
$795$	5.31823	0.188618
$796$	51.5857	1.82841
$797$	1.56756	0.0555257	0.0277629	−	0.999615i	$-0.491162\pi$
$797$	1.56756	0.0555257	0.0277629	+	0.999615i	$0.491162\pi$
$798$	3.44168	0.121834
$799$	−11.5872	−0.409926
$800$	−4.01045	−0.141791
$801$	−16.7421	−0.591553
$802$	−43.9560	−1.55214
$803$	7.31645	0.258192
$804$	−4.76368	−0.168002
$805$	8.40975	0.296405
$806$	−49.4731	−1.74262
$807$	−12.2323	−0.430596
$808$	−89.3569	−3.14357
$809$	48.0083	1.68788	0.843940	−	0.536437i	$-0.180230\pi$
$809$	48.0083	1.68788	0.843940	+	0.536437i	$0.180230\pi$
$810$	2.52275	0.0886403
$811$	23.0204	0.808355	0.404177	−	0.914681i	$-0.367558\pi$
$811$	23.0204	0.808355	0.404177	+	0.914681i	$0.367558\pi$
$812$	38.2305	1.34163
$813$	−27.8877	−0.978064
$814$	−8.79860	−0.308391
$815$	−17.0608	−0.597615
$816$	8.91050	0.311930
$817$	15.7360	0.550532
$818$	3.07312	0.107449
$819$	5.44168	0.190148
$820$	−45.5679	−1.59130
$821$	47.4418	1.65573	0.827864	−	0.560928i	$-0.189556\pi$
$821$	47.4418	1.65573	0.827864	+	0.560928i	$0.189556\pi$
$822$	−19.2028	−0.669776
$823$	48.0905	1.67633	0.838165	−	0.545416i	$-0.183628\pi$
$823$	48.0905	1.67633	0.838165	+	0.545416i	$0.183628\pi$
$824$	−12.3906	−0.431648
$825$	1.00000	0.0348155
$826$	−17.8532	−0.621193
$827$	26.9026	0.935496	0.467748	−	0.883862i	$-0.345065\pi$
$827$	26.9026	0.935496	0.467748	+	0.883862i	$0.345065\pi$
$828$	−36.7023	−1.27549
$829$	18.0592	0.627223	0.313611	−	0.949551i	$-0.398461\pi$
$829$	18.0592	0.627223	0.313611	+	0.949551i	$0.398461\pi$
$830$	−24.0143	−0.833548
$831$	−8.34518	−0.289491
$832$	−13.7081	−0.475244
$833$	1.41028	0.0488634
$834$	23.5031	0.813844
$835$	−0.866594	−0.0299897
$836$	−5.95397	−0.205923
$837$	3.60382	0.124566
$838$	−5.93068	−0.204872
$839$	6.74623	0.232906	0.116453	−	0.993196i	$-0.462848\pi$
$839$	6.74623	0.232906	0.116453	+	0.993196i	$0.462848\pi$
$840$	5.96443	0.205792
$841$	47.7361	1.64607
$842$	47.8244	1.64814
$843$	18.1998	0.626835
$844$	−105.748	−3.64000
$845$	−16.6119	−0.571466
$846$	20.7275	0.712625
$847$	1.00000	0.0343604
$848$	−33.6018	−1.15389
$849$	−7.49021	−0.257063
$850$	−3.55779	−0.122031
$851$	−29.3307	−1.00544
$852$	20.4917	0.702033
$853$	9.12097	0.312296	0.156148	−	0.987734i	$-0.450092\pi$
$853$	9.12097	0.312296	0.156148	+	0.987734i	$0.450092\pi$
$854$	−8.89621	−0.304422
$855$	1.36426	0.0466566
$856$	−79.7911	−2.72720
$857$	−40.8651	−1.39593	−0.697963	−	0.716134i	$-0.745910\pi$
$857$	−40.8651	−1.39593	−0.697963	+	0.716134i	$0.745910\pi$
$858$	−13.7280	−0.468666
$859$	−6.54852	−0.223433	−0.111716	−	0.993740i	$-0.535635\pi$
$859$	−6.54852	−0.223433	−0.111716	+	0.993740i	$0.535635\pi$
$860$	50.3393	1.71656
$861$	10.4411	0.355833
$862$	−82.9538	−2.82542
$863$	32.9504	1.12164	0.560822	−	0.827937i	$-0.310485\pi$
$863$	32.9504	1.12164	0.560822	+	0.827937i	$0.310485\pi$
$864$	−4.01045	−0.136438
$865$	−10.0628	−0.342145
$866$	23.5454	0.800104
$867$	−15.0111	−0.509804
$868$	15.7280	0.533843
$869$	4.55832	0.154630
$870$	22.0991	0.749228
$871$	−5.93971	−0.201260
$872$	61.3084	2.07617
$873$	16.2630	0.550418
$874$	−28.9437	−0.979035
$875$	−1.00000	−0.0338062
$876$	31.9309	1.07884
$877$	44.4377	1.50055	0.750277	−	0.661124i	$-0.229920\pi$
$877$	44.4377	1.50055	0.750277	+	0.661124i	$0.229920\pi$
$878$	−42.1325	−1.42190
$879$	−5.15983	−0.174037
$880$	−6.31823	−0.212988
$881$	48.6954	1.64059	0.820295	−	0.571941i	$-0.193809\pi$
$881$	48.6954	1.64059	0.820295	+	0.571941i	$0.193809\pi$
$882$	−2.52275	−0.0849453
$883$	14.7954	0.497906	0.248953	−	0.968516i	$-0.419913\pi$
$883$	14.7954	0.497906	0.248953	+	0.968516i	$0.419913\pi$
$884$	33.4927	1.12648
$885$	−7.07689	−0.237887
$886$	24.7023	0.829891
$887$	−21.0707	−0.707484	−0.353742	−	0.935343i	$-0.615091\pi$
$887$	−21.0707	−0.707484	−0.353742	+	0.935343i	$0.615091\pi$
$888$	−20.8022	−0.698075
$889$	12.8687	0.431603
$890$	−42.2361	−1.41576
$891$	1.00000	0.0335013
$892$	11.4470	0.383273
$893$	11.2090	0.375096
$894$	−35.6641	−1.19279
$895$	−2.42024	−0.0808998
$896$	14.3760	0.480267
$897$	−45.7632	−1.52799
$898$	92.2205	3.07744
$899$	31.5691	1.05289
$900$	4.36426	0.145475
$901$	−7.50022	−0.249868
$902$	−26.3404	−0.877039
$903$	−11.5345	−0.383843
$904$	−49.4668	−1.64524
$905$	−2.54191	−0.0844959
$906$	19.0867	0.634114
$907$	7.04732	0.234002	0.117001	−	0.993132i	$-0.462672\pi$
$907$	7.04732	0.234002	0.117001	+	0.993132i	$0.462672\pi$
$908$	−13.1923	−0.437802
$909$	14.9816	0.496910
$910$	13.7280	0.455078
$911$	41.7472	1.38315	0.691573	−	0.722307i	$-0.256918\pi$
$911$	41.7472	1.38315	0.691573	+	0.722307i	$0.256918\pi$
$912$	−8.61970	−0.285427
$913$	−9.51910	−0.315036
$914$	47.4242	1.56865
$915$	−3.52640	−0.116579
$916$	−14.1282	−0.466808
$917$	11.4239	0.377249
$918$	−3.55779	−0.117425
$919$	−2.65284	−0.0875092	−0.0437546	−	0.999042i	$-0.513932\pi$
$919$	−2.65284	−0.0875092	−0.0437546	+	0.999042i	$0.513932\pi$
$920$	−50.1594	−1.65371
$921$	16.8859	0.556408
$922$	−86.0187	−2.83288
$923$	25.5505	0.841006
$924$	4.36426	0.143574
$925$	3.48771	0.114675
$926$	15.6616	0.514673
$927$	2.07742	0.0682315
$928$	−35.1312	−1.15324
$929$	−33.7286	−1.10660	−0.553299	−	0.832983i	$-0.686631\pi$
$929$	−33.7286	−1.10660	−0.553299	+	0.832983i	$0.686631\pi$
$930$	9.09152	0.298123
$931$	−1.36426	−0.0447118
$932$	−78.7149	−2.57839
$933$	−15.0633	−0.493151
$934$	−8.09205	−0.264780
$935$	−1.41028	−0.0461212
$936$	−32.4565	−1.06087
$937$	−27.4371	−0.896330	−0.448165	−	0.893951i	$-0.647922\pi$
$937$	−27.4371	−0.896330	−0.448165	+	0.893951i	$0.647922\pi$
$938$	2.75364	0.0899094
$939$	−14.8687	−0.485223
$940$	35.8577	1.16955
$941$	11.5725	0.377251	0.188626	−	0.982049i	$-0.439597\pi$
$941$	11.5725	0.377251	0.188626	+	0.982049i	$0.439597\pi$
$942$	54.4844	1.77520
$943$	−87.8075	−2.85941
$944$	44.7134	1.45530
$945$	−1.00000	−0.0325300
$946$	29.0985	0.946075
$947$	11.0719	0.359789	0.179894	−	0.983686i	$-0.442424\pi$
$947$	11.0719	0.359789	0.179894	+	0.983686i	$0.442424\pi$
$948$	19.8937	0.646117
$949$	39.8138	1.29241
$950$	3.44168	0.111663
$951$	31.0015	1.00529
$952$	−8.41154	−0.272619
$953$	−48.3609	−1.56656	−0.783281	−	0.621667i	$-0.786456\pi$
$953$	−48.3609	−1.56656	−0.783281	+	0.621667i	$0.786456\pi$
$954$	13.4166	0.434377
$955$	−24.0899	−0.779532
$956$	41.2137	1.33295
$957$	8.75991	0.283168
$958$	25.5434	0.825270
$959$	7.61187	0.245800
$960$	2.51910	0.0813036
$961$	−18.0125	−0.581049
$962$	−47.8792	−1.54369
$963$	13.3778	0.431095
$964$	73.1720	2.35671
$965$	−7.77401	−0.250254
$966$	21.2157	0.682604
$967$	−38.9904	−1.25385	−0.626924	−	0.779081i	$-0.715686\pi$
$967$	−38.9904	−1.25385	−0.626924	+	0.779081i	$0.715686\pi$
$968$	−5.96443	−0.191704
$969$	−1.92399	−0.0618075
$970$	41.0274	1.31731
$971$	−56.7487	−1.82115	−0.910577	−	0.413340i	$-0.864362\pi$
$971$	−56.7487	−1.82115	−0.910577	+	0.413340i	$0.864362\pi$
$972$	4.36426	0.139984
$973$	−9.31645	−0.298672
$974$	64.5119	2.06710
$975$	5.44168	0.174273
$976$	22.2806	0.713184
$977$	−33.9990	−1.08772	−0.543862	−	0.839174i	$-0.683039\pi$
$977$	−33.9990	−1.08772	−0.543862	+	0.839174i	$0.683039\pi$
$978$	−43.0402	−1.37627
$979$	−16.7421	−0.535079
$980$	−4.36426	−0.139411
$981$	−10.2790	−0.328184
$982$	39.0221	1.24525
$983$	−3.52088	−0.112299	−0.0561494	−	0.998422i	$-0.517882\pi$
$983$	−3.52088	−0.112299	−0.0561494	+	0.998422i	$0.517882\pi$
$984$	−62.2755	−1.98527
$985$	0.425797	0.0135670
$986$	−31.1659	−0.992526
$987$	−8.21622	−0.261525
$988$	−32.3996	−1.03077
$989$	97.0019	3.08448
$990$	2.52275	0.0801782
$991$	35.2790	1.12068	0.560338	−	0.828264i	$-0.310671\pi$
$991$	35.2790	1.12068	0.560338	+	0.828264i	$0.310671\pi$
$992$	−14.4529	−0.458881
$993$	13.6597	0.433477
$994$	−11.8452	−0.375706
$995$	−11.8200	−0.374720
$996$	−41.5438	−1.31637
$997$	22.6176	0.716306	0.358153	−	0.933663i	$-0.383407\pi$
$997$	22.6176	0.716306	0.358153	+	0.933663i	$0.383407\pi$
$998$	1.79739	0.0568954
$999$	3.48771	0.110346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.w.1.1	✓	5
3.2	odd	2		3465.2.a.bm.1.5		5
5.4	even	2		5775.2.a.cg.1.5		5
7.6	odd	2		8085.2.a.bv.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.w.1.1	✓	5	1.1	even	1	trivial
3465.2.a.bm.1.5		5	3.2	odd	2
5775.2.a.cg.1.5		5	5.4	even	2
8085.2.a.bv.1.1		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52275 q^{2} +1.00000 q^{3} +4.36426 q^{4} -1.00000 q^{5} -2.52275 q^{6} +1.00000 q^{7} -5.96443 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.52275 q^{2} +1.00000 q^{3} +4.36426 q^{4} -1.00000 q^{5} -2.52275 q^{6} +1.00000 q^{7} -5.96443 q^{8} +1.00000 q^{9} +2.52275 q^{10} +1.00000 q^{11} +4.36426 q^{12} +5.44168 q^{13} -2.52275 q^{14} -1.00000 q^{15} +6.31823 q^{16} +1.41028 q^{17} -2.52275 q^{18} -1.36426 q^{19} -4.36426 q^{20} +1.00000 q^{21} -2.52275 q^{22} -8.40975 q^{23} -5.96443 q^{24} +1.00000 q^{25} -13.7280 q^{26} +1.00000 q^{27} +4.36426 q^{28} +8.75991 q^{29} +2.52275 q^{30} +3.60382 q^{31} -4.01045 q^{32} +1.00000 q^{33} -3.55779 q^{34} -1.00000 q^{35} +4.36426 q^{36} +3.48771 q^{37} +3.44168 q^{38} +5.44168 q^{39} +5.96443 q^{40} +10.4411 q^{41} -2.52275 q^{42} -11.5345 q^{43} +4.36426 q^{44} -1.00000 q^{45} +21.2157 q^{46} -8.21622 q^{47} +6.31823 q^{48} +1.00000 q^{49} -2.52275 q^{50} +1.41028 q^{51} +23.7489 q^{52} -5.31823 q^{53} -2.52275 q^{54} -1.00000 q^{55} -5.96443 q^{56} -1.36426 q^{57} -22.0991 q^{58} +7.07689 q^{59} -4.36426 q^{60} +3.52640 q^{61} -9.09152 q^{62} +1.00000 q^{63} -2.51910 q^{64} -5.44168 q^{65} -2.52275 q^{66} -1.09152 q^{67} +6.15484 q^{68} -8.40975 q^{69} +2.52275 q^{70} +4.69534 q^{71} -5.96443 q^{72} +7.31645 q^{73} -8.79860 q^{74} +1.00000 q^{75} -5.95397 q^{76} +1.00000 q^{77} -13.7280 q^{78} +4.55832 q^{79} -6.31823 q^{80} +1.00000 q^{81} -26.3404 q^{82} -9.51910 q^{83} +4.36426 q^{84} -1.41028 q^{85} +29.0985 q^{86} +8.75991 q^{87} -5.96443 q^{88} -16.7421 q^{89} +2.52275 q^{90} +5.44168 q^{91} -36.7023 q^{92} +3.60382 q^{93} +20.7275 q^{94} +1.36426 q^{95} -4.01045 q^{96} +16.2630 q^{97} -2.52275 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * q^99

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